Voltage conversion apparatus and method

ABSTRACT

A body force per unit mass acting on mobile charge carriers within a first electrically conducting material is configured to induce at least one region of accumulation of charge within at least a portion of the first material. The magnitude of the associated change in the voltage between two given points within the first material is a function of the relevant electrical properties of the material. A second electrically conducting material can be electrically coupled to the first material via a first electrical contact. The relevant electrical properties of the second material can be configured to be different to the relevant electrical properties of the first material. The voltage difference between the two points in the first material can be different to the voltage difference between two equivalent points in the second material. The difference in the voltage difference can be employed to increase the voltage of mobile charge carriers within a portion of an open or closed electrical circuit relative to another portion of said circuit. A voltage conversion apparatus and method can be used to convert thermal energy into electrical energy, for example.

CLAIM OF PRIORITY

The present patent application is a continuation of, and claims thebenefit of priority from, U.S. patent application Ser. No. 16/452,518,filed on Jun. 25, 2019, which further claims priority from U.S.Provisional Patent Application No. 62/763,638 filed on Jun. 25, 2018.The contents of the above identified applications are incorporatedherein by reference for all purposes to the extent that such subjectmatter is not inconsistent herewith.

FIELD

The invention relates to apparatuses and methods for modifying thepotential energy of mobile charge carriers.

BACKGROUND

In conventional voltage conversion apparatuses, such as voltageregulators, or DC-DC converters, the output power is typically less thanor equal to the input power.

In conventional thermoelectric generators, a difference in temperaturebetween a first thermal reservoir and a second thermal reservoir isrequired in order to convert thermal energy into electricity.

SUMMARY

Provided is an apparatus and method for voltage conversion. A body forceper unit mass acting on mobile charge carriers within a firstelectrically conducting material is configured to induce at least oneregion of accumulation of charge within at least a portion of anelectrically insulated portion of the first material. A region ofaccumulation of charge can be positively or negatively charged, and cancomprise a depletion or an accumulation of mobile charge carriers. Thefirst material can comprise a first electrical contact and a secondelectrical contact, where the first electrical contact is at a differentvoltage than the second electrical contact. At least a portion of thevoltage difference between the first and second contact can beassociated with a region of accumulation of charge. The magnitude of thechange in the voltage between two given points within the first materialis a function of the relevant electrical properties of the material.

A second electrically conducting material can be electrically connectedto the first material via the first electrical contact. The relevantelectrical properties of the second material can be configured to bedifferent to the relevant electrical properties of the first material.The voltage difference between the first and second electrical contactin the first material can, at least in theory, be different to thevoltage difference between two equivalent points in the second material.This difference in the voltage difference can be employed to increasethe voltage of mobile charge carriers within a portion of an open orclosed electrical circuit relative to another portion of said circuit.

In analogy to the depletion of mobile charge carriers at the interfaceof a p-type and n-type semiconductor, a region of accumulation of chargeis referred to as a “depletion region” herein. Note that a depletionregion, as used herein, can also comprise an accumulation of mobilecharge carriers.

The set of relevant electrical properties can comprise the number ofdonor atoms per unit volume within a material, where a donor atom candonate a mobile charge carrier, such as an electron, and becomepositively charged, or ionized, in the process. The set of relevantelectrical properties can comprise the number of acceptor atoms per unitvolume within a material, where an acceptor atom can accept a mobilecharge carrier, such as an electron, and become negatively charged, orionized, in the process. An acceptor atom can also be considered to be adonor of a hole. Note that a “hole” is a quasiparticle which ispositively charged, as described in the field of semiconductors.

The set of relevant electrical properties can comprise the nominalnumber of mobile charge carriers per unit volume within a material. Forexample, the set of relevant electrical properties can comprise thenumber of free electrons, or the number of conduction electrons, perunit volume within a material. The nominal case can be the case in whichthere is no accumulation of net charge within a material, for example.For instance, there are three conduction electrons per atom in aneutrally charged Aluminium, and one conduction electron per atom inneutrally charged copper. The set of relevant electrical properties cancomprise the average amount of charge per mobile charge carrier.

The set of relevant electrical properties can comprise the temperatureof the material. The set of relevant electrical properties can comprisethe absolute permittivity within the material.

The set of relevant electrical properties can comprise a wide variety ofother properties for a subset of embodiments, such as the electricalresistivity of a material, the effective mass of mobile charge carriers,or the thermal conductivity of a material.

In general, the set of relevant electrical properties can comprise thelength or the extent of a region of accumulation of charge within thespecified material along the average path of mobile charge carriersthrough a region of accumulation of charge, i.e. through the so-calleddepletion region. This length or extent of the depletion region isreferred to as the “thickness” of the depletion region herein. Note thatthe thickness of the depletion region is also a function of theexternally applied electric field. The set of relevant electricalproperties are therefore not limited to the properties of a material perse.

The mobile charge carriers can be electrons, holes, or positively ornegatively charged ions, for example. The body force per unit mass canbe electromagnetic, inertial, or gravitational in nature, for example.The first material can comprise an electrically conducting material,such as a metal, a semiconductor, or a liquid solution comprisingpositively or negatively charged ions. The first material can alsocomprise a gas, such as a thermal or nonthermal plasma.

A voltage conversion apparatus and method can be used in electricitygenerators, voltage amplifiers, or voltage regulators, for example. Avoltage conversion apparatus and method can also be employed to convertthermal energy into electricity, for instance. The thermal energy from asingle thermal reservoir is sufficient for the generation ofelectricity.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings described herein are for illustration purposes only. Thedrawings are not intended to limit the scope of the present disclosure.

FIG. 1 shows a cross-sectional view of one embodiment of the invention.

FIG. 2 shows a plot of the approximate value of several physicalparameters as a function of position.

FIG. 3 shows a diagram of a parallel arrangement of the conversionportion/apparatus of FIG. 1, according to embodiment of the invention.

DETAILED DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a cross-sectional view of one embodiment of the invention.

Bulk material 1 is an electrical insulator such as glass or a ceramic.Bulk material 1 also provides structural support to the electricalconductors it interfaces with. In other embodiments, bulk material 1 canalso be a semiconductor with a low electrical conductivity compared tothe other conductors of the embodiment.

The particular embodiment shown in FIG. 1 comprises several collectionsof negative charge, such as first top charge collection 4, second topcharge collection 5, as well as several collections of positive charge,such as first bottom charge collection 6, and second bottom chargecollection 7. In other embodiments, the polarity can be reversed, i.e.the top charge collections can be positively charged, and the bottomcharge collections can be negatively charged.

Each charge collection, such as charge collection 4, has a rectangularcross-section when viewed along the Y-direction. In other embodiments, acharge collection can have any geometry, such as a square or polygonalcross-sectional geometry when viewed along the Y-direction or theZ-direction. For example, a charge collection can be cylindrical inshape, with a circular cross-section when viewed along the Y-direction.

In the embodiment shown, first top charge collection 4 is configuredidentically to the second top charge collection 5, and the first bottomcharge collection 6 is configured identically to the second bottomcharge collection 7. In other embodiments, this need not be the case.

In the embodiment shown, a charge collection comprises an electricallyconducting material, such as a metal, such as copper or silver. In otherembodiments, a charge collection can comprise any conducting material,such as graphene. In yet other embodiments, a charge collection cancomprise an insulating material, with individual charges embedded withinsaid material. In other words, the conductivity of the insulatingmaterial with respect to the embedded charges of a charge collection canbe negligible in some embodiments. For example, a charge collection cancomprise positively or negatively charged ions embedded within anelectrical insulator, such as glass.

During nominal operations, the amount of charge in a charge collectionscan remain substantially constant. In the embodiment shown in FIG. 1,the amount of charge in a charge collection, such as charge collection4, can also be regulated or controlled. This is useful for regulatingthe magnitude of the voltage conversion generated by the embodiment. Theamount of charge in a charge collection, i.e. the charge density, can beregulated by connecting a charge collection to a separate voltage sourceby means of an electrical conductor, such as a copper wire. By changingthe voltage of the separate voltage source, the amount of charge in acharge collection can be controlled. For example, the negative terminalof a voltage source can be electrically connected to first top chargecollection 4, and the positive terminal of a voltage source can beelectrically connected first bottom charge collection 6. A wide varietyof methods are available for regulating the voltage of such a separatevoltage source. Note that a top and bottom charge collection can beconsidered to be the charged plates of a capacitor, which is energizedby the separate voltage source. In other embodiments, the voltage sourceneed not be separate. In such embodiments, at least a portion of thevoltage difference between a top charge collection and a correspondingbottom charge collection can be generated by the embodiment itself, i.e.by the voltage difference between station 33 and station 26. The top andbottom charge collections can thus be considered to be the opposingcharge collections of a capacitor which is connected in parallel to anelectrical circuit which connects first outside contact 34 with secondoutside contact 35.

An electrical conductor 20 connects a first outside contact 34 with afirst conductor 8. Electrical conductor 20 can be a conductor such asgraphene, or a metal such as copper. In some embodiments, electricalconductor 20 can also be considered to be a superconductor. In FIG. 1,electrical conductor 20 is shown as a bold line for simplicity, and canbe considered to be an electrical wire. In some embodiments, electricalconductor 20 and first conductor 8 need not be distinguishable. In otherwords, electrical conductor 20 and first conductor 8 can be made of thesame material, such as copper, and can have a substantially identicallengthwise cross-sectional area and geometry.

First conductor 8 can comprise a conducting material such as graphene,or a metal such as copper or silver. First conductor 8 can also be anintrinsic semiconductor. First conductor 8 can also be an extrinsicsemiconductor, i.e. an n-type or p-type semiconductor. First conductor 8can also be doped with both n-type and p-type dopants, both of whichincrease the conductivity of a semiconductor.

First conductor 8 has a rectangular cross-section when viewed along theY-direction. In other embodiments, a first conductor 8 can have anycross-sectional geometry, such as a circular, square or polygonalcross-sectional geometry when viewed along the Y-direction.

An electrical conductor 22 is configured to connect station 29 of firstconductor 8 to station 30 of second conductor 14 via electricalcontacts, such as contact 23. As mentioned in the context of electricalconductor 20, electrical conductor 22 can be made of the same materialand can have the same lengthwise cross-sectional area as first conductor8. Electrical conductor 21 is configured in a similar manner aselectrical conductor 20 in the embodiment shown in FIG. 1.

Note that the terms “top” and “bottom” only refer to the locationrelative to a potential well produced by these collections of charge,and are not intended to indicate the position relative to a spatialcoordinate frame, such as the XYZ-frame shown. The potential energy of amajority mobile charge carrier in first conductor 8 or second conductor14 is defined to be lower at the bottom than it is at the top. Forinstance, when the polarity of the collections of charge is reversed,ceteris paribus, the terms are reversed, i.e. “top” can be replaced by“bottom”, and vice versa. By default, the charge carriers are assumed tobe negatively charged. In some embodiments, however, at least a portionof charge carriers can be positively charged.

Second conductor 14 can comprise a conducting material, where theaverage conductivity of the conductor along the path of current flowthrough the length of the conductor is smaller than the same averageconductivity associated with first conductor 8. Second conductor 14 canbe made of similar types of materials as first conductor 8, and viceversa. For example, second conductor 14 can be a semiconductor, such assilicon, and first conductor 8 can be a metal such as copper. Firstconductor 8 can also be a doped semiconductor, where the doping hasincreased the conductivity of first conductor 8 to a value greater thanthe conductivity of second conductor 14. In order to simplifymanufacturing, it can be desirable for first conductor 8 and secondconductor 14 to be made of the same original material, such as siliconor gallium arsenide. In this case, the amount of doping can beconfigured to be larger in the first conductor 8 such that theconductivity of the first conductor 8 is greater than the conductivityin the second conductor 14. Alternatively, the type of dopant material,i.e. the molecular species of the impurity, can be configured to achievethe same effect with respect to the relative conductivity of the firstconductor 8 and the second conductor 14. As long as this condition ismet, second conductor 14 and first conductor 8 can be made of anymaterial, such as a doped semiconductor material, an intrinsicsemiconductor material, or a conducting material such as metal. Othermethods are available for configuring or selecting the material of firstconductor 8 relative to the material of the second conductor 14 suchthat the conductivity of the first conductor 8 is greater than theconductivity in the second conductor 14. As is known in the art, theconductivity of a material is determined by a number of factors, such asthe concentration of mobile charge carriers per unit volume, or the meanfree path of a mobile charge carrier within a conductor, or thetemperature of the conductor, amongst other parameters. Note that thefirst conductor 8 and the second conductor 14 can be made of the samematerial in some embodiments, provided the principles of the inventionare applied. The mobile charges can be electrons or ions, for example.In the latter case, first conductor 8 or second conductor 14 can also bea liquid or a gas, through which the ions are able to diffuse.

Second conductor 14 has a rectangular cross-section when viewed alongthe Y-direction. In other embodiments, a second conductor 14 can haveany cross-sectional geometry, such as a circular, square or polygonalcross-sectional geometry when viewed along the Y-direction.

The first assembly 2 comprises the first top charge collection 4, thefirst conductor 8, and the first bottom charge collection 6. The secondassembly 3 comprises the second top charge collection 5, the secondconductor 14, and the second bottom charge collection 7.

The electrical conductor 20, the first conductor 8, the electricalconductor 22, the second conductor 14, the electrical conductor 21 forma portion of an electric circuit, denoted the “conversion portion”. Inthe embodiment shown in FIG. 1, this circuit is shown a closed circuitfor simplicity. In some embodiments an open circuit can be formedbetween station 33 and station 26. In some embodiments, a separateelectrical circuit, denoted the “load portion” 36 can be connected inparallel to the conversion portion. The two terminals of the loadportion can be connected to the two terminals of the conversion portion,i.e. to first outside contact 34 and second outside contact 35. For someembodiments, an electrical current can be made to flow through theconversion portion. For example, current can flow from the secondoutside contact 35, through electrical conductor 21, second conductor14, electrical conductor 22, first conductor 8, and electrical conductor20 to the first outside contact 34 during nominal operations, wherenominal operation involves a steady current flow. To close the currentloop, current also flows from first outside contact 34 through the loadportion 36 to the second outside contact 35 in this particular example.In some embodiments, at least a portion of the current flow is a resultof a larger voltage at first outside contact 34 compared to secondoutside contact 35, where the larger voltage is a consequence of theconfiguration of the embodiment shown in FIG. 1.

The load portion can comprise any electrical device. For example, theload portion can comprise a conductor with a non-negligible resistivity.In some embodiments, the load portion can also be considered to comprisea single, conventional resistor. The load portion can also compriseelectrical devices such as transistors, capacitors, or inductors. Theload portion can also comprise an antenna configured to generateelectromagnetic waves. The load portion can also comprise digitalelectronics, such as a microprocessor or computer. The load portion canalso comprise an electric motor 39 configured to do mechanical work“WOUT”. Note that electrical motors typically comprise heat exchangers,such as heat exchanger 40, in order to facilitate the flow of heat “QIN”between the electrical conductors and the outside environment. In thecase in which the mobile charge carriers perform work WOUT, the heat QINcan flow from the outside environment to the mobile charge carriers. Inthis manner, the conductors remain at a suitable temperature duringnominal operations, where suitability is determined by the objective andthe constraints of the particular application and the configuration ofthe embodiment. In the simplified embodiment shown in FIG. 1, the heatexchanger 40 comprises several fins, such as fin 43. A fin can comprisea thin circular metal plate, for example, where mobile charge carrierscan flow through the metal plate, and where the surface normal of theplanar plate is parallel to the X-axis. The outside environment cancomprise the air of the atmosphere, for instance. In some embodiments,heat can be exchanged between the heat exchanger and the outsideenvironment via natural convection, forced convection, thermalradiation, or thermal conduction, for instance. The electrical currentflowing through the conversion apparatus and the electrical load 36 canbe configured to also flow through the heat exchanger 40, in order tofacilitate the transfer of heat between the heat exchanger and themobile charge carriers. The load portion can comprise any electricaldevice capable of sustaining a voltage drop while a non-negligiblecurrent flows through the load portion. The load portion can comprise alight emitting diode.

In the following paragraphs, the origin of a voltage difference betweenthe first outside contact 34 and the second outside contact 35 will beexplained. For simplicity, the conversion portion is an open circuitthroughout this explanation, i.e. there is no current flow through theconversion portion. Note that, in the case in which current flows fromfirst outside contact 34 to second outside contact 35 through the loadportion, there is typically a decrease in the magnitude of the voltagedifference between the first outside contact 34 and the second outsidecontact 35 compared to the open circuit scenario shown in FIG. 1. Thisdecrease is due to a voltage drop within the conversion portion, whicharises from the internal resistance of the conductors within theconversion portion and the current flowing through the conversionportion.

Consider the first assembly 2. When considered in isolation, the firsttop collection of charge 4 and the first bottom collection of charge 6produce an electric field. In this “isolated case” the first topcollection of charge 4 and the first bottom collection of charge 6 aresurrounded by a vacuum. Consider a simplified scenario in which thefield lines are assumed to be parallel to the Y-axis at all times. Inthis scenario, the electric field lines are directed in the positiveY-direction in the region between the first top collection of charge 4and the first bottom collection of charge 6. The field is zero elsewherein this simplified scenario. In reality, due to the finite size of thetop and bottom charge collections, the field is non-uniform in magnitudeand direction, in particular at the edges of the charge collections andthe boundary of the “projected volume” between them, i.e. the volumeenclosed by the projection of the boundary of a top charge collectiononto the boundary of a bottom charge collection along the Y-direction.The aforementioned simplified scenario describes or reflects the generalnature of the field, however. To summarize, in the isolated case in thesimplified scenario, the magnitude of the electric field in theprojected volume of the first top collection of charge 4 and the firstbottom collection of charge 6 is uniform in space and time, and parallelto the Y-axis. The amount of charge in each charge collection is assumedto be constant in time and uniform in space throughout the chargecollection.

In transitioning from the isolated case to the actual case shown in FIG.1, consider the “reduced case” in which the isolated case is augmentedby the placement of the first conductor 8 in between the first topcollection of charge 4 and the first bottom collection of charge 6, asdepicted in FIG. 1. In the reduced case, the electrical conductors 20and 22 are not present. A portion of the mobile charges within firstconductor 8 experience a body force per unit mass due to the electricfield of the first top collection of charge 4 and the first bottomcollection of charge 6. As a result, the density of negative mobilecharges within first conductor 8 increases in the close proximity of thepositively charged first bottom collection of charge 6. Note that, in aperfect conductor, this accumulation of negative charge is negligiblythin along the Y-direction. In this case the charges can be consideredto accumulate at the surface of the first conductor 8 which faces thefirst bottom collection of charge 6. For illustrative purposes, in theembodiment shown in FIG. 1, first conductor 8 is not a perfectconductor, resulting in a small extent of the first bottom accumulationregion 12 along the Y-direction, denoted the “thickness” of theaccumulation region. First bottom boundary 13 schematically indicatesthe approximate extent of the first bottom accumulation region 12.Similarly, due to a conservation of charge, there is a positivelycharged first top depletion region 10, with a first top boundary 11. Inother embodiments, the thickness of the first top depletion region 10and the first bottom accumulation region 12 need not be identical. Dueto the electric field produced by the first top depletion region 10 andthe first bottom accumulation region 12 superimposed on the electricfield produced by the first top collection of charge 4 and the firstbottom collection of charge 6, the remaining portion of first conductor8 is neutrally charged in this configuration. This portion is denotedthe first neutral region 9.

Station 27 is located in first conductor 8 in negligibly close proximityto the top surface of first conductor 8, i.e. the surface facing thefirst top collection of charge 4, as indicated by the location of thelabel of station 27 in FIG. 1. Station 28 is located in the firstneutral region 9 at the location shown. Station 29 is located in firstconductor 8 in negligibly close proximity to the bottom surface of firstconductor 8, i.e. the surface facing the first bottom collection ofcharge 6.

The configuration of the second assembly 3 in a reduced case can bedescribed in a similar manner. The electric field produced by the secondtop collection of charge 5 and the second bottom collection of charge 7results in a redistribution of mobile charge carriers within secondconductor 14. This redistribution manifests itself in the form of apositively charged second top depletion region 16, with second topboundary 17 and a negatively charged second bottom accumulation region18, with second bottom boundary 19. Due to the electric field producedby the second top depletion region 16 and second bottom accumulationregion 18 superimposed on the electric field produced by the second topcollection of charge 5 and the second bottom collection of charge 7, theremaining portion of second conductor 14 is neutrally charged in thisconfiguration. This portion is denoted the second neutral region 15.

Station 30 is located in second conductor 14 in negligibly closeproximity to the bottom surface of second conductor 14, i.e. the surfacefacing the second bottom collection of charge 7, as indicated by thelocation of the label of station 30 in FIG. 1. Station 31 is located inthe second neutral region 15 at the location shown. Station 32 islocated in second conductor 14 in negligibly close proximity to the topsurface of second conductor 14, i.e. the surface facing the second topcollection of charge 5.

In accordance with some embodiments of the invention, the thickness ofthe second top depletion region 16 is larger than the thickness of thefirst top depletion region 10. In accordance with some embodiments ofthe invention, the thickness of the second bottom accumulation region 18is larger than the thickness of the first bottom accumulation region 12.In accordance with some embodiments of the invention, the sum of thethicknesses of the second bottom accumulation region 18 and the secondtop depletion region 16 is larger than the sum of the thicknesses of thefirst bottom accumulation region 12 and the first top depletion region10.

In some embodiments, this is accomplished at least in part by a largerelectrical conductivity associated with the first conductor 8 comparedto the second conductor 14 and an externally applied electric field. Inthe embodiment shown in FIG. 1, this external field is generated byfirst top collection of charge 4, second top collection of charge 5,first bottom collection of charge 6, and second bottom collection ofcharge 7.

In some embodiments the thickness of the first top depletion region 10is substantially equal to the thickness of the second top depletionregion 16, while the thickness of the first bottom accumulation region12 is smaller than the thickness of the second bottom accumulationregion 18. In some embodiments the thickness of the first top depletionregion 10 is smaller than the thickness of the second top depletionregion 16, while the thickness of the first bottom accumulation region12 is substantially equal to the thickness of the second bottomaccumulation region 18.

To transition from the reduced case to the actual case depicted in FIG.1, the electrical conductor 22 needs to be considered. The electricalconnection between stations 29 and 30 by electrical conductor 22 canhave an effect on the thickness and form of the first bottomaccumulation region 12 and the second bottom accumulation region 18. Forexample, a larger density of mobile charge carriers, such as electrons,at station 29 in the reduced case compared to station 30 can result inthe diffusion of charges from station 29 to station 30 in a conceptualtransition from the reduced case to the actual case, e.g. by closing ahypothetical switch between stations 29 and station 30. This increasesthe thickness of second bottom accumulation region 18 compared to thereduced case, and reduces the thickness of the first bottom accumulationregion 12 compared to the reduced case. This can increase the potentialenergy of a negatively charged mobile charge in the second neutralregion 15 compared to the reduced case. Similarly, this can reduce thepotential energy of a negatively charged mobile charge in the firstneutral region 9 compared to the reduced case. As a result, a netvoltage difference between the first neutral region 9 and the secondneutral region 15 can arise. The increased thickness of the secondaccumulation region 18 and the reduced thickness of the first bottomaccumulation region 12 results in an electric field being produced atthe interface between the first conductor 8 and the second conductor 14,between station 29 and station 30. As a result of this field, there is adrift current of mobile charges from station 30 to station 29, whichcancels the diffusion current of mobile charges from station 29 tostation 30 due to the aforementioned charge density difference betweenstation 29 and station 30. Once this new equilibrium is reached, theconceptual transition from the theoretical, reduced case to the actual,depicted, open-circuit case can be considered to be complete.

Note that the net voltage difference between the first neutral region 9and the second neutral region 15 in the open circuit, actual case can bezero or negative, because this voltage difference takes into account thecontact potential between the first conductor 8 and the second conductor14 in the open circuit scenario being considered. However, as soon asthe circuit is closed, any voltage difference associated with theelectrical contact between first conductor 8 and second conductor 14established by electrical conductor 22 is offset by the electricalcontact between the same second conductor 14 and the same firstconductor 8 established by electrical conductors 21 and 20 and the loadportion of the closed circuit. In other words, the contact potentialscancel in a closed circuit.

Note that, in some embodiments, the net diffusion of charges fromstation 29 to station 30 throughout a conceptual transition from thereduced case to the actual case can also be zero or negative. Forexample, the contact potential between first conductor 8 and the secondconductor 14 can produce an electric field on the diffusion current pathbetween station 30 and station 29, which prevents the net motion ofcharges between station 29 and station 30 in a conceptual transitionfrom the reduced case to the actual, open circuit case shown in FIG. 1.In such configurations, the distribution of charge in the firstconductor 8 and second conductor 14 in the reduced case can besubstantially equal to the distribution of charge in the actual case.

Note that the current path through the embodiment in FIG. 1 is U-shapedand the potential well is \-shaped. In other words, the depth of thepotential well increases in the negative Y-direction since the potentialenergy of a mobile charge carrier in the electric field in the isolatedcase decreases in the negative Y-direction. In other embodiments, thecurrent path can be unidirectional, i.e. I-shaped, and the potentialwell can be >-shaped. Note that, in both of these types of embodiments,the potential well along the current path is >-shaped. The latterembodiment can be explained as follows. The central axis of the secondconductor can coincide with the central axis of the first conductor,with the two conductors being offset in the Y-direction. The connectionbetween the first conductor and the second conductor can be formed by anelectrical conductor which is parallel to the Y-axis, similarly toelectrical conductor 22, which is parallel to the X-axis. Saidelectrical conductor can pass through an insulated portion of a bottomcollection of charge. Alternatively, the first conductor and secondconductor can be in direct physical contact, where the location ofcontact is surrounded by an insulated bottom collection of charge. Inother words, the bottom collection of charge can be configured tosurround the region of contact between the first and second conductorlike a toroid surrounds a central cylinder. Note that the bottomcollection of charge and the first and second conductor need to beconfigured in a manner in which the bottom accumulation region of eachconductor, i.e. both the first conductor and the second conductor, spansthe entire cross-sectional area of each conductor when viewed along theY-direction. In other words, the minimum sum of the thicknesses of bothbottom accumulation regions should be non-zero, where the minimum iscalculated over the cross-section of the first or second conductorsviewed in the Y-direction. In such embodiments, the first top collectionof charge is located at the top of the I-shaped arrangement of the firstand second conductors, and the second top collection of charge islocated at the bottom of the I-shaped arrangement, with the bottomcollection of charge being located half-way along the I-shapedarrangement when the length of the first and second conductors along theY-direction is identical.

In some embodiments, the bulk material 1 is electrostatically insulatedfrom the surroundings. This insulation can comprise a conductingmaterial, such as a metal. In this case, the embodiment can beconfigured in a manner in which the net charge enclosed within bulkmaterial 1 is zero during nominal operations. This could mitigate anyelectrostatic interference of the field generated by a top or bottomcollection of charge within bulk material 1 by any external electricfields.

In some embodiments, first top charge collection 4 and second top chargecollection 5 are joined together to form a single, top collection ofcharge. Similarly, a single bottom collection of charge can beconfigured in the same manner.

In some embodiments, the may only be a single type of collection ofcharge. For example, some embodiments comprise only one or more bottomcollections of charge, without there being a single top collection ofcharge. In some embodiments, the top and bottom collections of chargeneed not contain the same amount of charge.

FIG. 2 shows a plot of the approximate value of several physicalparameters as a function of position.

For simplicity, the contact potential between the second conductor 14and the first conductor 8 is assumed to produce an electric fieldbetween the contact potential between the second conductor 14 and thefirst conductor 8, such that there is no diffusion of mobile chargecarriers from the first conductor 8 to the second conductor 14, or viceversa, when the transition from the reduced case to the actual casedepicted in FIG. 1 is made. In other words, the thickness of the secondbottom accumulation region 18 and the first bottom accumulation region12 is substantially identical for the aforementioned theoretical,reduced case and the depicted actual, open circuit case.

Axis 50, which is parallel to the X-axis, denotes the magnitude of avalue of a physical parameter corresponding to a specified line. Axis51, which is parallel to the Y-axis, denotes the location of the valueof the physical parameter of a specified line at a position along theY-axis, where the position is measured relative to the origin of axis 50and axis 51.

Line 52 denotes the value of the average charge density in first topcollection of charge 4, or second top collection of charge 5 at a givenlocation along the Y-axis. In this simplified model, the amount ofcharge per unit volume in a first top collection of charge is assumed tobe constant throughout a collection of charge. In some embodiments, orin practice, this need not be the case. For example, the charge densitycan decrease throughout a top collection of charge in the positiveY-direction.

Line 53 denotes the average charge density in first bottom collection ofcharge 6, or second bottom collection of charge 7 at a given locationalong the Y-axis. As before, the charge density throughout a bottomcollection of charge is assumed to be constant. In some embodiments, orin practice, the charge density can increase throughout a bottomcollection of charge in the positive Y-direction.

Line 54 denotes the average charge density in the first depletion region10 in first conductor 8 at a given location along the Y-axis. Line 55denotes the average charge density in the first accumulation region 12in first conductor 8 at a given location along the Y-axis. Line 56denotes the average charge density in the second depletion region 16 insecond conductor 14 at a given location along the Y-axis. Line 57denotes the average charge density in the second accumulation region 18in second conductor 14 at a given location along the Y-axis. As before,the average charge density in a depletion or accumulation region neednot be uniform in practice, or in other embodiments. For example, theaverage charge density can decrease more gradually in a directiontowards the neutral region of the corresponding conductor, or in adirection towards the other accumulation region or other depletionregion of the corresponding conductor. For instance, in someembodiments, the magnitude of the average charge density can besubstantially constant in the second top depletion region 16, as shownby line 56, but increase in at an increasing rate in the negativeY-direction in the second bottom accumulation region 18. In someembodiments the increase occurs in exponential fashion. For otherembodiments the magnitude of the average charge density can increase inat an increasing rate in the positive Y-direction in a top accumulationregion. In some embodiments the magnitude of the average charge densityincreases in at an increasing rate in both the accumulation region andthe depletion region of a specified conductor, such as the secondconductor 14, where the increase is measured relative to the neutralregion or the interface between the accumulation region and thedepletion region.

During nominal operations, some embodiments of the invention areconfigured in a manner in which there are a sufficient number of mobilecharge carriers at stations 32 and 27, or stations 30 and 29, orstations 33 and 26 for current to flow through the conversion portion assoon as a closed circuit is formed by attaching a load portion betweenfirst outside contact 34 and second outside contact 35.

In some embodiments, electrical conductor 20 is not attached to firstconductor 8 at station 27, but rather at station 28. In other words,electrical conductor 20 is electrically connected to first neutralregion 9. In some embodiments, electrical conductor 21 is attached tosecond conductor 14 at station 31 as opposed to station 32. In otherwords, electrical conductor 21 is electrically connected to secondneutral region 15. When the majority of mobile electrical charges arenegatively charged, such as in the case in which the mobile charges areelectrons, such a configuration can reduce the internal resistance ofthe conversion apparatus, where the internal resistance is theresistance associated with a current flowing through the depictedconversion portion. Note that, in some embodiments, this reduction ininternal resistance also applies to the case in which the majority ofmobile charges are positively charged. In other embodiments, theelectrical conductors 20, 21, and 22 can be connected to the first orsecond conductors at any suitable locations along the Y-direction, i.e.along the depth of the potential well.

In some embodiments, the electrical contact 23 in the first conductor 8need not lie in the region of accumulation of charge 12, but can lie inthe neutrally charged region 9 of the first conductor 8. In suchembodiments, the first conductor 8 can be a metal, for example. In suchembodiments the electrical coupling 22 can connect a nominally neutrallycharged region in the first conductor 8, such as the region at station28, with a nominally charged region in the second conductor 14, such asthe region of accumulation of charge 18. In such embodiments the secondconductor can be a semiconductor, for example. In such embodiments theinternal resistance of the conversion apparatus can be reduced further,since the resistance of metals such as copper is typically smallcompared to the resistance of semiconductors.

Note that the total amount of charge per unit cross-sectional areaviewed along the Y-axis contained within the entire first accumulationregion 12 and the entire second accumulation region 18 is substantiallyidentical. The same is true for the first depletion region 10 and thesecond depletion region 16. This is a consequence of Gauss' law and theassumptions employed in the aforementioned simplified scenario.

The collections of charge and the accumulation and depletion regionsproduce an electric field. The value of the electric field associatedwith first assembly 2 is represented by line 58 and line 59. These linesindicate the component of the electric field directed in the negativeY-direction, where the electric field is measured along the longitudinalcenterline of first conductor 8, which is parallel to the Y-axis.Similarly, the value of the electric field associated with secondassembly 3 is represented by line 60 and line 61.

The potential energy of a negatively charged mobile charge diffusingfrom station 26 to station 33 via stations 27, 28, 29, 30, 31, and 32 isindicated by line 62. The potential energy at station 33 is larger thanat station 26. Thus, when the open circuit is closed with a loadportion, the mobile negative charges will move through the load portionfrom station 33 to station 26, and through the depicted conversionportion from station 26 to station 33 to complete the circuit.

The voltage at station 27 is larger than the voltage at station 32. Dueto symmetry, this voltage difference is maintained between first outsidecontact 34 and second outside contact 35, which are located far enoughfrom the collections of charge, such as first top charge collection 4,such that the ambient electric field is negligible. Note that, in someembodiments, the thickness of a neutral region, such as second neutralregion 15, is zero. Thus, a low voltage at station 33 can be consideredto have been converted by the embodiment of the invention into a highervoltage at station 34.

In some embodiments, several conversion portions, such as the conversionportion shown in FIG. 1, are electrically connected in series. In otherwords, the second outside electrical contact 35 of a first conversionportion is connected to the first electrical outside contact 34 of asecond conversion portion.

In some embodiments, as illustrated in FIG. 3, several conversionportions, such as the conversion portion shown in FIG. 1, areelectrically connected in parallel. In other words, the second outsideelectrical contact 35 of a first conversion portion is connected to thesecond outside electrical contact 35 of a second conversion portion, andthe first electrical outside contact 34 of a first conversion portion isconnected to the first electrical outside contact 34 of a secondconversion portion. In general, the load portion of a given conversionportion can comprise at least one other conversion portion of the sameor similar type as the given conversion portion.

In some embodiments, the extent of a conductor, such as first conductor8, in the Y-direction, denoted the conductor “height”, is on the orderof one nanometer. In some embodiments, this length is on the order ofone micrometer. In some embodiments this length is within several ordersof magnitude of one micrometer. In some embodiments, this length is onthe order of a centimeter. In some embodiments, this length is on theorder of a meter. This length can be take any suitable value in otherembodiments.

The extent of a conductor, such as first conductor 8, in theX-direction, denoted the conductor “width”, is on the order of onenanometer in some embodiments. The width of first conductor 8 need notbe equal to the width of second conductor 14. The width can take anysuitable value. In some embodiments, the cross-sectional area of aconductor, such as first conductor 8, viewed along the Y-direction is onthe order of a square centimeter. In some embodiments, this area is onthe order of a square meter. The area can take any suitable value.

Embodiments of the invention can be manufactured using a wide variety ofmethods and processes. Such methods area known in the art ofsemiconductor manufacturing, for example.

The change in the potential energy of a mobile charge carrier diffusingor moving through a region of accumulation of charge, such as depletionregion 10, or accumulation region 12, or depletion region 16, oraccumulation region 18, is a function of a wide variety of “relevantproperties”, or “relevant parameters”. In accordance with someembodiments of the invention, at least one relevant property of thefirst conductor 8 is different than the same relevant property in thesecond conductor 14. In this manner, the change in the potential energyof a mobile charge carrier moving or diffusing through a region ofaccumulation of charge is different in the first conductor and thesecond conductor for a given change in position in the potential wellformed by the body force generating apparatus. In the embodiment in FIG.1, the body force generating apparatus is embodied by the electric fieldgenerating apparatus, which comprises collections of charge 4, 5, 6, and7. The body force generating apparatus is configured to generate anelectrical body force per unit mass acting on mobile charge carriers inthe first conductor 8 and second conductor 14.

In other embodiments, other types of body forces per unit mass can beconfigured to act on the mobile charge carriers within a conductor. Forexample, a body force generating apparatus can comprise a magnetic fieldgenerating apparatus, where at least a portion of the body force perunit mass acting on the mobile charge carriers in a first and/or secondconductor can be magnetic in nature.

A body force generating apparatus can comprise a gravitational fieldgenerating apparatus, where at least a portion of the body force perunit mass acting on the mobile charge carriers in a first and/or secondconductor can be gravitational in nature. In this embodiment, the bodyforce generating apparatus can comprise a mass, such as the mass ofplanet earth, located below the first conductor 8 and second conductor14, similar to collections of charge 6 or 7, as shown in FIG. 1. Inembodiments in which the mobile charge carriers carry a net charge, asis the case of mobile electrons in a fixed lattice of positively chargednuclei, the regions of accumulation of charge on opposing ends of areservoir, such as the reservoir formed by first conductor 8, generatean electrical field within the remaining portion of the reservoir, wherethe electric field cancels the body force per unit mass, such as thegravitational body force per unit mass, acting on the mobile chargecarriers. The neutrally charged portion of the reservoir, such asneutrally charged portion 28, can comprise an electric field in suchembodiments, which is in contrast to the neutrally charged portion 28shown in FIG. 1, in which the body force generating apparatus comprisesan electrical field generating apparatus. Note that, in general, it issufficient for the mobility of one type of mobile charge carrier to bedifferent to the mobility of another type of mobile charge carrierwithin a material. In general, both the positively charged chargecarriers and the negatively charged charge carriers in a reservoir canbe mobile charge carriers, provided the relevant properties of bothcharge carriers are different. This ensures that a body force generatingapparatus can be configured to generate a region of accumulation of netcharge within a reservoir in the scenario in which the body force perunit mass acting on both types of mobile charge carriers is identical.

A body force generating apparatus can comprise an accelerationgenerating apparatus, where at least a portion of the body force perunit mass acting on the mobile charge carriers in a first and/or secondconductor can be inertial in nature. For example, the reservoir ofmobile charge carriers, such as the reservoir formed by the firstconductor 8 or second conductor 14, can be accelerated in an inertialreference frame. The mobile charge carriers contained within thereservoirs thus experience an effective or perceived accelerationrelative to the boundaries or the walls of the reservoir. Theacceleration in an inertial frame can be due to a translationalaccelerating motion, or a rotational motion of the reservoir, forexample. In the latter case, the reservoirs can be rotated about an axisparallel to the X-axis, where the axis is located in the positiveY-direction of station 27, for instance. In such embodiments the firstconductor 8 and/or the second conductor can comprise a plasma, forinstance.

As mentioned, the set of relevant properties can comprise the electricalresistivity of a material. The electrical resistivity in the secondconductor 14 can be larger than in the first conductor 8, resulting in alarger thickness of the regions of accumulation of charge in the secondconductor 14 than in the first conductor 8, as shown, resulting in alarger potential energy of mobile charge carriers at station 31 than atstation 28, or a larger potential energy at station 32 than at station27. Note that the electrical resistivity is a function of a large numberof material properties. For example, the cross-sectional area of thesecond conductor 14 can be smaller than the cross-sectional area of thefirst conductor 8, resulting in a larger resistivity of the secondconductor compared to the first conductor. The cross-sectional area canbe measured along the direction of current flow, for instance.

The set of relevant properties can also comprise the number of mobilecharge carriers per unit volume in a material. For instance, in FIG. 1,the number of mobile charge carriers per unit volume in the firstconductor 8 can be larger than in the second conductor 14. In particularthe thickness of a region of accumulation of mobile charge carriers,such as the thickness of accumulation region 12 or accumulation region18, is a function of the number of mobile charge carriers per unitvolume. In a semiconductor, the set of relevant properties can comprisethe number of donor or acceptor atoms per unit volume. Note that a holein a semiconductor can also be considered to be a mobile charge carrier.In a metal, the set of relevant properties can comprise the number offree electrons or the number of conducting electrons per unit volume. Ina solution, or in a gas, the set of relevant properties can comprise thenumber of ions per unit volume, for example.

The set of relevant properties can also comprise the number of fixedcharge carriers per unit volume in a material. In a solid, a fixedcharge carrier can be a positively charged nucleus of an atom, forexample. For instance, in FIG. 1, the number of fixed charge carriersper unit volume in the first conductor 8 can be larger than in thesecond conductor 14. In particular the thickness of a region ofdepletion of mobile charge carriers, such as the thickness of depletionregion 10 or depletion region 16, is a function of the number of fixedcharge carriers per unit volume. In a metal or semiconductor, the set ofrelevant properties can also comprise the number of atoms per unitvolume, for example. In a doped semiconductor, the set of relevantproperties can comprise the number of donor or acceptor atoms per unitvolume.

The set of relevant properties can also comprise the temperature of amaterial. For example, the temperature in the second conductor 14 can belarger than the temperature in the first conductor 8. As a result, thethickness of the region of an accumulation of charge in the firstconductor 8 can be larger in the second conductor 14 than in the firstconductor 8, ceteris paribus. The temperature is particularly relevantin determining the thickness of a region of accumulation of mobilecharge carriers. In a subset of embodiments, the temperature differencebetween said conductors can be maintained by a first thermal reservoirwhich is thermally coupled to the first conductor 8, and a secondthermal reservoir which is thermally coupled to the second conductor 14,for example. The temperature of the second thermal reservoir can belarger than the temperature of the first thermal reservoir. In such anembodiment, the voltage conversion apparatus can be operated in asimilar manner as a conventional thermoelectric generator, such as athermoelectric generator employing the Peltier effect.

The set of relevant properties can also comprise the absolutepermittivity of a material. In the case in which the body forcegenerating apparatus comprises an electrical field generating apparatus,and in the case in which the electric field generating apparatuscomprises a fixed collection of charge, the absolute permittivity in thesecond conductor 14 can be smaller than in the first conductor 8. Inthis case the average potential energy of mobile charge carriers atstation 31 can be larger than at station 28. Note that in someembodiments the thickness of the accumulation region 18 in the secondconductor 14 can be smaller than the thickness of the accumulationregion 12 in the first conductor 8, despite the potential energy ofmobile charge carriers being larger at station 31 than at station 28.

In the case in which the body force generating apparatus comprises anelectrical field generating apparatus, and in the case in which theelectric field generating apparatus comprises a variable collection ofcharge, such as a collection of charge on an electrical conductor, wherethe electrical charge is supplied by an external electrical voltagesource such as a battery, the absolute permittivity in the secondconductor 14 can be larger than in the first conductor 8. In this casethe average potential energy of mobile charge carriers at station 31 canbe larger than at station 28. In such embodiments the thickness of theaccumulation region 18 in the second conductor 14 can be larger than thethickness of the accumulation region 12 in the first conductor 8, asshown in FIG. 1.

The set of relevant properties can also comprise the average amount ofcharge carried by a mobile charge carrier in a material. For example,the average amount of charge carried by a mobile charge carrier in thesecond conductor 14 can be smaller than in the first conductor 8. Thiscan result in a larger potential energy of mobile charge carriers atstation 31 than at station 28 in an open circuit scenario.

The set of relevant properties can also comprise the strength of theelectric field at the boundary of a material. The boundary for thesecond conductor 14, denoted the “second boundary”, can be the boundaryof the second conductor 14 and the insulating material 1 at the boundaryfacing a collection of charge, such as collection of charge 7 orcollection of charge 5, i.e. at a boundary for which the surface normalis parallel to the Y-axis. The boundary for the first conductor 8,denoted the “first boundary”, can be the boundary of the first conductor8 and the insulating material 1 at the boundary facing a collection ofcharge, such as collection of charge 6 or collection of charge 4, i.e.at a boundary for which the surface normal is parallel to the Y-axis.For example, the strength of the electric field within the secondconductor 14 at the second boundary can be larger than the strength ofthe electric field within the first conductor 8. As a result, thethickness of the associated region of accumulation of charge can belarger in the second conductor 14 than the thickness of the associatedand corresponding region of accumulation of charge in the firstconductor 8, and the average potential energy of the mobile chargecarriers at station 31 can be larger than at station 28.

The aforementioned relevant properties are particularly relevant in thecase in which the regions of accumulation of charge are substantiallyisothermal. In some embodiments, the change in the density of mobilecharge carriers throughout a region of accumulation of charge can bedescribed as an adiabatic or polytropic process. In some embodiments,the change in density can be described as an isobaric process, forinstance. A non-isothermal region of accumulation of charge can be foundin a first or second conductor in the case in which the thermalconductivity of the first or second conductor is comparatively low, forinstance. A nonthermal plasma or a semiconductor can exemplify suchbehavior. Note that, in the case in which there is a net current flow, aregion of accumulation of charge is less likely to be isothermal due tothe change in the potential energy of mobile charge carriers and theassociated change in temperature of mobile charge carriers, as well asother thermal effects such as Joule heating.

The set of relevant properties can also comprise the effective mass of amobile charge carrier within a material. For example, the effective massof a mobile charge carrier in the second conductor 14 can be smallerthan the effective mass of a mobile charge carrier in the firstconductor 8 in a subset of embodiments. In some embodiments, the changein the density of mobile charge carriers throughout a region ofaccumulation of charge can be described as an adiabatic process, forexample.

In some embodiments, an electrical switch can also be located betweenstation 33 and station 26, where the switch can be employed to regulatethe current flow though the electrical load 36, for example. A variableresistance can also be located between station 33 and station 26, wherethe resistance can be employed to regulate the rate of current flowthough the electrical load 36, or the voltage across the electricalload, for example. In some embodiments a voltage regulator can beemployed to regulate the voltage across the electrical load 36.

The mobile charge carriers can comprise electrons, holes, or positivelyor negatively charged ions.

Electrical conductor 22 can be described as an electrical coupling.Electrical load 36 and heat exchanger 40 can also be considered to beconstituent parts of an electrical coupling.

In other embodiments, the insulated collections of charge, such ascollections of charge 4, 5, 6, or 7, can be embedded within the firstconductor 8 and within the second conductor 14. A collection of chargecan comprise multiple insulated individual collections of charge, forinstance. This can allow mobile charge carriers to diffuse through thefirst or second material of the first and second conductor,respectively, and through the insulated collections of charge embeddedtherein.

In some embodiments, the collections of charge can be located adjacentto the first or second conductors, as opposed to above and below thefirst and second conductors. In other words, the collection of charge 4can be located in the positive and negative X-direction of the firstconductor 8 as opposed to in the positive Y-direction of first conductor8. For instance, the collection of charge 4 can be annular in shape, andcan be configured to envelop a first conductor 8 which is circular incross-section. In a subset of such embodiments, the long axis of a firstconductor and a second conductor which are circular in cross-section canbe coincident and parallel. Several such first and second conductors canbe connected in series. The junction between a first conductor and asecond conductor can be enveloped by an annular collection of charge,where the charge carried by a collection of charge for adjacentjunctions can be of an opposing sign, and where the first and secondconductors pass through the center of an annular collection of charge.The first and second conductor can be cylindrical in shape, and can beof a similar radius in a subset of embodiments. In other embodiments,the radius of the second conductor can be smaller than in the firstconductor, ceteris paribus. The insulated collection of charge at ajunction can be configured to be symmetric across the plane of ajunction in some embodiments. As before, the collections of charge canbe electrically insulated from the first and second conductors by anelectrical insulator such as glass, plastic, or PVC. At junction, afirst conductor can be in direct contact with a second conductor,allowing mobile charge carriers to move between the first and secondconductors. As before, the thickness of a region of accumulation ofcharge at a junction between a first conductor and a second conductorcan be larger in a second conductor than in the first conductor. Asbefore, the mobile charge carriers can experience a greater change intheir potential energy throughout a second conductor compared to a firstconductor. As before, this can be due to the relevant properties in thesecond conductor being different compared to the first conductor. Asbefore, the external, insulated collections of charge can comprise fixedelectrical charges embedded within a material, or can compriseelectrical conductors which are charged by an external electrical energysupply, such as a battery, a capacitor, an inductor, or a thermoelectricgenerator. Note that the insulated collections of charge can beelectrically charged, at least in part, by the same potential energyconversion apparatus of which it is part, or the same voltage conversionapparatus in which the collection of charge is employed as a body forcegenerating apparatus.

In a semiconductor, the rate of change of the density of mobile chargecarriers can be described by the following continuity equations:

$J_{n} = {{{e\mu}_{n}{nE}} + {e\mspace{14mu} D_{n}\frac{dn}{dx}}}$$J_{p} = {{{e\mu}_{p}{pE}} - {e\mspace{14mu} D_{p}\frac{dp}{dx}}}$

In these equations I_(n) is the current density of electrons, e is thecharge per electron, μ_(n) is the electron mobility, n is density ofmobile charge carriers per unit volume, i.e. the density of mobileelectrons per unit volume, E is the local electric field strength, whichis a function of position, D_(n) is the mobile electron diffusionconstant, and x is the position in space.

Similarly I_(p) is the current density of holes, e is the charge perhole, μ_(p) is the hole mobility, p is density of mobile charge carriersper unit volume, i.e. the density of mobile holes per unit volume, E isthe local electric field strength, which is a function of position,D_(p) is the mobile hole diffusion constant, and x is the position inspace.

In the case in which the behavior of mobile charge carriers within aregion of accumulation of charge can be described as an isothermalbehavior, the following Einstein relations apply:

$D_{n} = {\frac{kT}{e}\mu_{n}}$ $D_{p} = {\frac{kT}{e}\mu_{p}}$

In these equations T is the temperature of the material. Note that thelocal electric field is a function of the adjacent accumulation ofcharge, such as the accumulation of mobile charge carriers. Theinfluence of neighboring accumulations of charge can be expressed interms of Gauss' law. This results in the following Poisson's equation:

${ɛ_{r}ɛ_{0}\frac{\partial E}{\partial x}} = {e\left( {p - n + N_{D} - N_{A}} \right)}$

In this Poisson's equation, the product ε_(γ)ε_(o) is the absolutepermittivity, where ε_(γ) is the relative permittivity, and ε₀ is thepermittivity of the vacuum. N_(D) is the number of donor atoms per unitvolume for n-type doping, and N_(A) is the number of acceptor atoms perunit volume for p-type doping.

By taking a spatial derivative of the above continuity equations for thecase in which the current density of electrons and holes is zero, i.e.in the open circuit case, and by using Poisson's equation to solve forthe electric field, the density of mobile charge carriers as a functionof position within a region of accumulation of mobile charge carrierscan be calculated. Note that the density of mobile charge carriers cansaturate in an accumulation or depletion region. The variation of thedensity of mobile charge carriers for other materials, such as metals orplasmas, can be calculated in similar fashion.

ASPECTS OF THE INVENTION

The invention is further defined by the following aspects.

Aspect 1. A potential energy modification apparatus, wherein thepotential energy modification apparatus comprises: a body forcegenerating apparatus; a first material, wherein the first material iselectrically conducting, wherein the body force generating apparatus canbe configured to induce a region of accumulation of charge within thefirst material, and wherein the first material comprises a first pointand a second point

Aspect 2. The apparatus of aspect 1, wherein the apparatus furthercomprises a second material, wherein the second material is electricallyconducting, wherein the body force generating apparatus can beconfigured to induce a region of accumulation of charge within thesecond material, and wherein the second material comprises a first pointand a second point

Aspect 3. The apparatus of aspect 2, wherein the second point in thesecond material is electrically coupled to the second point in the firstmaterial

Aspect 4. The apparatus of aspect 1, wherein a mobile charge carrier atthe first point in the first material can have a different potentialenergy than a mobile charge carrier at the second point in the firstmaterial on average in an open circuit scenario

Aspect 5. The apparatus of aspect 2, wherein a mobile charge carrier atthe first point in the second material can have a different potentialenergy than a mobile charge carrier at the second point in the secondmaterial on average in an open circuit scenario

Aspect 6. The apparatus of aspect 2, wherein a mobile charge carrier atthe first point in the second material can have substantially the samepotential energy as a mobile charge carrier at the second point in thesecond material on average in an open circuit scenario

Aspect 7. The apparatus of aspect 1, wherein the second point in thefirst material lies within a region of accumulation of charge

Aspect 8. The apparatus of aspect 2, wherein the second point in thesecond material lies within a region of accumulation of charge

Aspect 9. The apparatus of aspect 2, wherein the second point in thesecond material lies within a neutrally charged region

Aspect 10. The apparatus of aspect 2, wherein the first point in thesecond material is electrically coupled to the first point in the firstmaterial

Aspect 11. The apparatus of aspect 3, wherein the first point in thesecond material is electrically coupled to the first point in the firstmaterial

Aspect 12. The apparatus of any one of aspects 3, 10, or 11, wherein theelectrical coupling comprises an electrical conductor

Aspect 13. The apparatus of any one of aspects 3, 10, or 11, wherein theelectrical coupling comprises a capacitor

Aspect 14. The apparatus of any one of aspects 3, 10, or 11, wherein theelectrical coupling comprises an inductor

Aspect 15. The apparatus of any one of aspects 3, 10, or 11, wherein theelectrical coupling comprises an alternating current

Aspect 16. The apparatus of any one of aspects 3, 10, or 11, wherein theelectrical coupling comprises a direct current

Aspect 17. The apparatus of any one of aspects 3, 10, or 11, wherein theelectrical coupling comprises the transfer of electrical power betweenthe two points in space or time

Aspect 18. The apparatus of aspect 4, wherein at least a portion of thechange in the potential energy is due to the region of accumulation ofcharge within the first material

Aspect 19. The apparatus of aspect 5, wherein at least a portion of thechange in the potential energy is due to the region of accumulation ofcharge within the second material

Aspect 20. The apparatus of aspect 1, wherein the first point in thefirst material lies within a region of accumulation of charge

Aspect 21. The apparatus of aspect 1, wherein the first point in thefirst material lies within a neutrally charged region

Aspect 22. The apparatus of aspect 2, wherein the first point in thesecond material lies within a region of accumulation of charge

Aspect 23. The apparatus of aspect 2, wherein the first point in thesecond material lies within a neutrally charged region

Aspect 24. The apparatus of any one of aspects 2 or 3, wherein thethickness of the region of accumulation of charge within the secondmaterial is smaller than the thickness of the region of accumulation ofcharge within the first material

Aspect 25. The apparatus of any one of aspects 2 or 3, wherein thechange in the potential energy of a mobile charge carrier moving throughthe region of accumulation of charge within the first material is largerin magnitude than the change in the potential energy of a mobile chargecarrier moving through the region of accumulation of charge within thesecond material.

Aspect 26. The apparatus of any one of aspects 2 or 3, wherein therelevant properties of the second material are different than therelevant properties in the first material

Aspect 27. The apparatus of any one of aspects 2 or 3, wherein therelevant material properties of the second material are different thanthe relevant material properties in the first material

Aspect 28. The apparatus of any one of aspects 2 or 3, wherein thechange in the potential energy of a mobile charge carrier moving throughat least a portion of the region of accumulation of charge between thefirst point in the first material and the second point in the firstmaterial is larger in magnitude than the change in the potential energyof a mobile charge carrier moving through at least a portion of theregion of accumulation of charge between the first point in the secondmaterial and the second point in the second material

Aspect 29. The apparatus of any one of aspects 2 or 3, wherein at leasta portion of the first material is electrically insulated from a secondmaterial

Aspect 30. The apparatus of aspect 3, wherein the body force generatingapparatus comprises an electric field generating apparatus, wherein atleast a portion of the body force is electric in nature

Aspect 31. The apparatus of aspect 30, wherein the electric fieldgenerating apparatus comprises a collection of charge

Aspect 32. The apparatus of aspect 30, wherein the electric fieldgenerating apparatus comprises an electrical conductor can be configuredto be able to be positively or negatively charged

Aspect 33. The apparatus of aspect 32, wherein the electrical conductorand an electrical power source, wherein the electrical power source canbe configured to positively or negatively charge the electricalconductor

Aspect 34. The apparatus of aspect 33, wherein the electrical powersource can comprise a battery

Aspect 35. The apparatus of aspect 33, wherein the electrical powersource can comprise a capacitor

Aspect 36. The apparatus of aspect 33, wherein the electrical powersource can comprise an inductor

Aspect 37. The apparatus of aspect 33, wherein the electrical powersource can comprise an electricity generator

Aspect 38. The apparatus of aspect 37, wherein the electricity generatorcan comprise an electric motor

Aspect 39. The apparatus of aspect 37, wherein the electricity generatorcan comprise a thermoelectric generator

Aspect 40. The apparatus of aspect 37, wherein at least a portion of theelectricity is generated by any one of the potential energy modificationapparatuses of any one of all other aspects of the invention.

Aspect 41. The apparatus of aspect 3, wherein the body force generatingapparatus comprises a gravitational field generating apparatus, andwherein at least a portion of the body force is gravitational in nature

Aspect 42. The apparatus of aspect 3, wherein the body force generatingapparatus comprises a magnetic field generating apparatus, and whereinat least a portion of the body force is magnetic in nature

Aspect 43. The apparatus of aspect 1, wherein the body force generatingapparatus comprises an electromagnetic field generating apparatus, andwherein at least a portion of the body force is electromagnetic innature

Aspect 44. The apparatus of aspect 3, wherein the body force generatingapparatus comprises an electromagnetic field generating apparatus, andwherein at least a portion of the body force is electromagnetic innature

Aspect 45. The apparatus of aspect 3, wherein the body force generatingapparatus comprises an accelerating apparatus, wherein the acceleratingapparatus is configured to accelerate the first material or the secondmaterial in an inertial frame, and wherein at least a portion of thebody force is inertial in nature

Aspect 46. The apparatus of aspect 45 wherein the acceleration iscentripetal in nature

Aspect 47. The apparatus of aspect 45 wherein the acceleration istranslational in nature

Aspect 48. The apparatus of aspect 1 wherein the first materialcomprises mobile charge carriers

Aspect 49. The apparatus of aspect 2 wherein the second materialcomprises mobile charge carriers

Aspect 50. The apparatus of any one of aspects 1, 2, 48, or 49, whereinthe mobile charge carriers comprise electrons

Aspect 51. The apparatus of any one of aspects 1, 2, 48, or 49, whereinthe mobile charge carriers comprise positively or negatively chargedions

Aspect 52. The apparatus of any one of aspects 1, 2, 48, or 49, whereinthe mobile charge carriers comprise holes

Aspect 53. The apparatus of aspect 1, wherein the first materialcomprises a metal

Aspect 54. The apparatus of aspect 1, wherein the first materialcomprises a semiconductor

Aspect 55. The apparatus of aspect 1, wherein the first materialcomprises a solid

Aspect 56. The apparatus of aspect 1, wherein the first materialcomprises a fluid

Aspect 57. The apparatus of aspect 56, wherein the first materialcomprises a liquid

Aspect 58. The apparatus of aspect 56, wherein the first materialcomprises a solution, wherein the mobile charge carriers comprisepositively or negatively charged ions located within the solution

Aspect 59. The apparatus of aspect 56, wherein the first materialcomprises a gas

Aspect 60. The apparatus of aspect 59 wherein the first materialcomprises a plasma

Aspect 61. The apparatus of aspect 60 wherein the first materialcomprises a nonthermal plasma

Aspect 62. The apparatus of aspect 60 wherein the first materialcomprises a thermal plasma

Aspect 63. The apparatus of aspect 54, wherein the first materialcomprises an intrinsic semiconductor

Aspect 64. The apparatus of aspect 54, wherein the first materialcomprises an n-type semiconductor

Aspect 65. The apparatus of aspect 54, wherein the first materialcomprises a p-type semiconductor

Aspect 66. The apparatus of aspect 2, wherein the second materialcomprises a metal

Aspect 67. The apparatus of aspect 2, wherein the second materialcomprises a semiconductor

Aspect 68. The apparatus of aspect 2, wherein the second materialcomprises a solid

Aspect 69. The apparatus of aspect 2, wherein the second materialcomprises a fluid

Aspect 70. The apparatus of aspect 69, wherein the second materialcomprises a liquid

Aspect 71. The apparatus of aspect 69, wherein the second materialcomprises a solution, wherein the mobile charge carriers comprisepositively or negatively charged ions located within the solution

Aspect 72. The apparatus of aspect 69, wherein the second materialcomprises a gas

Aspect 73. The apparatus of aspect 72 wherein the second materialcomprises a plasma

Aspect 74. The apparatus of aspect 73 wherein the second materialcomprises a nonthermal plasma

Aspect 75. The apparatus of aspect 73 wherein the second materialcomprises a thermal plasma

Aspect 76. The apparatus of aspect 67, wherein the second materialcomprises an intrinsic semiconductor

Aspect 77. The apparatus of aspect 67, wherein the second materialcomprises an n-type semiconductor

Aspect 78. The apparatus of aspect 67, wherein the second materialcomprises a p-type semiconductor

Aspect 79. The apparatus of any one of aspects 2 or 3, wherein thenumber of mobile charge carriers per unit volume within the firstmaterial is smaller than the number of mobile charge carriers per unitvolume within the second material

Aspect 80. The apparatus of aspect 79, wherein the mobile chargecarriers are electrons

Aspect 81. The apparatus of any one of aspects 2 or 3, wherein theelectrical conductivity within the first material is smaller than theelectrical conductivity in the second material

Aspect 82. The apparatus of any one of aspects 2 or 3, wherein thebehavior of the mobile charge carriers within the first material or thesecond material is substantially isothermal in an open circuit scenario

Aspect 83. The apparatus of any one of aspects 2 or 3, wherein thebehavior of the mobile charge carriers within the first material or thesecond material is not isothermal in an open circuit scenario

Aspect 84. The apparatus of any one of aspects 2 or 3, wherein theabsolute permittivity within the first material is smaller than theabsolute permittivity within the second material

Aspect 85. The apparatus of any one of aspects 2 or 3, wherein theabsolute permittivity within the first material is larger than theabsolute permittivity within the second material

Aspect 86. The apparatus of aspect 84, wherein the body force generatingapparatus comprises an electric field generating apparatus, wherein theelectric field generating apparatus comprises a charge collectioncomprising charges fixed in space and time

Aspect 87. The apparatus of aspect 85, wherein the body force generatingapparatus comprises an electric field generating apparatus, wherein theelectric field generating apparatus comprises a charge collectioncomprising an electrical conductor connected to a voltage supply

Aspect 88. The apparatus of any one of aspects 2, 3, or 84, wherein thethickness of the region of accumulation of charge within the secondmaterial is larger than the thickness of the region of accumulation ofcharge within the first material

Aspect 89. The apparatus of any one of aspects 86, 87, 88, wherein thematerial properties of the first material and the second material areidentical with the exception of the difference in the permittivity

Aspect 90. The apparatus of any one of aspects 2 or 3, wherein the firstmaterial and the second material comprise an n-type semiconductor, andwherein the number of donor atoms per unit volume is larger in thesecond material than in the first material

Aspect 91. The apparatus of any one of aspects 2 or 3, wherein the firstmaterial and the second material comprise a p-type semiconductor, andwherein the number of acceptor atoms per unit volume is larger in thesecond material than in the first material

Aspect 92. The apparatus of any one of aspects 2 or 3, wherein the firstmaterial and the second material comprise a p-type semiconductor, andwherein the number of acceptor atoms per unit volume is larger in thesecond material than in the first material

Aspect 93. The apparatus of any one of aspects 2 or 3, wherein thenumber of atoms per unit volume is larger in the second material than inthe first material

Aspect 94. The apparatus of any one of aspects 2 or 3, wherein thenumber of atoms per unit volume is larger in the second material than inthe first material

Aspect 95. The apparatus of any one of aspects 2 or 3, wherein the firstmaterial comprises a semiconductor, and wherein the second materialcomprises a metal

Aspect 96. The apparatus of any one of aspects 2 or 3, wherein thetemperature in the first material is larger than the temperature in thesecond material

Aspect 97. The apparatus of aspect 96, wherein the material propertiesof the first material and the second material are identical with theexception of the difference in the temperature

Aspect 98. The apparatus of any one of aspects 2 or 3, wherein thetemperature in the first material is smaller than the temperature in thesecond material

Aspect 99. The apparatus of aspect 98, wherein the material propertiesof the first material and the second material are different, even withthe exception of the difference in the temperature

Aspect 100. The apparatus of any one of aspects 2 or 3, wherein theaverage charge carried by a mobile charge carrier in the first materialis smaller than in the second material

Aspect 101. The apparatus of aspect 100, wherein the material propertiesof the first material and the second material are identical with theexception of the difference in the average charge carried by a mobilecharge carrier

Aspect 102. The apparatus of any one of aspects 2 or 3, wherein theaverage charge carried by a mobile charge carrier in the first materialis larger than in the second material

Aspect 103. The apparatus of aspect 102, wherein the material propertiesof the first material and the second material are the different, evenwith the exception of the difference in the average charge carried by amobile charge carrier

Aspect 104. The apparatus of any one of aspects 2 or 3, wherein themobile charge carrier is a quasiparticle

Aspect 105. The apparatus of any one of aspects 2 or 3, wherein themobile charge carrier is a virtual particle

Aspect 106. The apparatus of any one of aspects 2 or 3, wherein the bodyforce generating apparatus comprises an electric field generatingapparatus, wherein the electric field strength at a boundary of thefirst material and within the first material is larger than the electricfield strength at the boundary of the second material and within thesecond material, where the electrical field at the boundary forms aboundary condition for the electric field generated within a region ofaccumulation of charge within a material, and thereby determines thethickness of the region of accumulation of charge, amongst otherparameters

Aspect 107. The apparatus of aspect 106, wherein the properties of thefirst material and the second material are identical with the exceptionof the difference in electric field strength at a boundary of the firstmaterial and a boundary of the second material

Aspect 108. The apparatus of aspect 107, wherein the electrical couplingbetween the second point in the first material and the second point inthe second material comprises an electrical conductor

Aspect 109. The apparatus of aspect 108, wherein the electricalconductor is a metal

Aspect 110. The apparatus of any one of aspects 2 or 3, wherein theaverage effective mass of a mobile charge carrier within the firstmaterial is smaller than in the second material

Aspect 111. The apparatus of any one of aspects 3, 10, or 11, whereinthe electrical coupling comprises a superconductor

Aspect 112. The apparatus of any one of aspects 3, 10, or 11, whereinthe electrical coupling comprises a metal

Aspect 113. The apparatus of any one of aspects 3, 10, or 11, whereinthe electrical coupling comprises an electrical load

Aspect 114. The apparatus of any one of aspects 3, 10, or 11, whereinthe electrical coupling comprises a heat exchanger

Aspect 115. The apparatus of aspect 113, wherein the electrical loadcomprises a resistor

Aspect 116. The apparatus of aspect 113, wherein the electrical loadcomprises an electric motor

Aspect 117. The apparatus of aspect 113, wherein the electrical loadcomprises a computer or microprocessor

Aspect 118. The apparatus of aspect 113, wherein the electrical loadcomprises an electrical switch

Aspect 119. The apparatus of aspect 114, wherein the heat exchanger isconfigured to deliver heat from the environment to the mobile chargecarriers

Aspect 119B. The apparatus of any one of aspects 2 or 3, wherein theaverage potential energy of mobile charge carriers at the first point inthe first material is larger than the average potential energy of mobilecharge carriers at the first point in the second material

Aspect 119C. The apparatus of aspect 11, wherein mobile charge carrierscan flow from the first point in the second material to the second pointin the second material, and via the first electrical coupling from thesecond point in the second material to the second point in the firstmaterial, and from the second point in the first material to the firstpoint in the first material, and via the second electrical coupling fromthe first point in the first material to the first point in the secondmaterial, thus completing the electrical circuit.

Aspect 119D. The apparatus of aspect 11, wherein an electrical currentcan flow from the first point in the first material to the second pointin the first material, and via the first electrical coupling from thesecond point in the first material to the second point in the secondmaterial, and from the second point in the second material to the firstpoint in the second material, and via the second electrical couplingfrom the first point in the second material to the first point in thefirst material, thus completing the electrical circuit.

Aspect 119E. The apparatus of any one of aspects 119C or 119D, whereinat least a portion of the electrical energy of the mobile chargecarriers is provided by thermal energy of the mobile charge carriers

Aspect 120. A system comprising two or more of the potential energymodification apparatuses of any one of aspects 1 to 119, and aspects119B-E

Aspect 121. A system comprising two or more of the potential energymodification apparatuses of aspect 2

Aspect 122. A system comprising two or more of the potential energymodification apparatuses of aspect 3

Aspect 123. The system of aspect 122, wherein the first point in thefirst material of a first potential energy modification apparatus iselectrically coupled to the first point in the second material of asecond potential energy modification apparatus

Aspect 124. The system of aspect 120, wherein a first potential energymodification apparatus is electrically coupled in series with a secondpotential energy modification apparatus

Aspect 125. The system of aspect 122, wherein the first point in thefirst material of a first potential energy modification apparatus iselectrically coupled to the first point in the first material of asecond potential energy modification apparatus, and wherein the firstpoint in the second material of a first potential energy modificationapparatus is electrically coupled to the first point in the secondmaterial of a second potential energy modification apparatus

Aspect 126. The system of aspect 120, wherein a first potential energymodification apparatus is electrically coupled in parallel with a secondpotential energy modification apparatus

Aspect 127. A method of potential energy modification, comprising:providing a potential energy modification apparatus or systems of anyone of aspects 1 to 126, including aspects 119B-E.

Aspect 128. A method of potential energy modification, comprising:providing and operating a potential energy modification apparatus orsystem of any one of aspects 1 to 126, including aspects 119B-E, andselecting or providing the material properties of the materials ofpotential energy modification apparatus or system of any one of aspects1 to 126, including aspects 119B-E

Aspect 129. A method of potential energy modification, comprising:providing a body force generating apparatus; providing a first material,wherein the first material is electrically conducting, employing thebody force generating apparatus to induce a region of accumulation ofcharge within the first material, wherein the first material comprises afirst point and a second point

Aspect 130. The method of aspect 129, wherein the method furthercomprises: providing a second material, wherein the second material iselectrically conducting, wherein the body force generating apparatus caninduce a region of accumulation of charge within the second material,wherein the second material comprises a first point and a second point

Aspect 131. The method of aspect 130, wherein the method furthercomprises electrically coupling the second point in the second materialto the second point in the first material

Aspect 132. The method of aspect 131, wherein the method furthercomprises configuring the body force generating apparatus, such that theaverage potential energy of mobile charge carriers at the first point inthe first material is different than the average potential energy ofmobile charge carriers at the first point in the second material

Aspect 133. The method of aspect 131, wherein the method furthercomprises selecting or providing the material properties of the firstmaterial relative to the material properties of the second material,such that the average potential energy of mobile charge carriers at thefirst point in the first material is different than the averagepotential energy of mobile charge carriers at the first point in thesecond material

Aspect 134. The method of aspect 131, wherein the method furthercomprises electrically coupling the first point in the first materialwith the first point in the second material, thereby forming a closedelectrical circuit

Aspect 135. The method of aspect 133, wherein the selecting or providingof the material properties of the first material relative to thematerial properties of the second material comprises selecting orproviding a first material with a larger number of mobile chargecarriers per unit volume relative to the second material

Aspect 136. The method of aspect 133, wherein the selecting or providingof the material properties of the first material relative to thematerial properties of the second material comprises selecting orproviding a first material with a larger number of mobile chargecarriers per unit volume relative to the second material

Aspect 137. The method of aspect 133, wherein the selecting or providingof the material properties comprises selecting or providing a firstmaterial with a smaller electrical conductivity than the second material

Aspect 138. The method of aspect 133, wherein the selecting or providingof the material properties comprises thermally coupling the firstmaterial to a first thermal reservoir, and the thermally coupling thesecond material to a second thermal reservoir, wherein the temperatureof the first material is different to the temperature of the secondmaterial

Aspect 139. The method of aspect 133, wherein the selecting or providingof the material properties comprises manipulating the temperature of thefirst material or the second material, such that the temperature of thefirst material is different to the temperature of the second material

Aspect 140. The method of aspect 133, wherein the selecting or providingof the material properties comprises selecting of providing a firstmaterial with a different absolute permittivity than the second material

Aspect 141. The method of aspect 131, wherein the method furthercomprises providing or manipulating the properties of the first materialor the second material, or configuring the body force generatingapparatus, such that the thickness of the region of accumulation ofcharge in the first material is larger than the thickness of the regionof accumulation of charge in the second material

Aspect 141B. The method of aspect 131, wherein the selecting orproviding of the material properties comprises selecting of providing afirst material with a different average charge per charge carrier thanthe second material

Aspect 141C. The method of aspect 131, wherein the selecting orproviding of the material properties comprises selecting of providing afirst material with a different average effective mass per chargecarrier than the second material

Aspect 142. The method of aspect 134, wherein the method furthercomprises allowing electrical current to flow through the electricalcircuit

Aspect 143. The method of aspect 132, wherein the method furthercomprises including or providing an electrical load within or to theelectrical circuit

Aspect 144. The method of aspect 143, wherein the electrical loadcomprises an electric motor, a microprocessor, a computer, or a resistor

Aspect 145. The method of aspect 129, wherein providing the body forcegenerating apparatus comprises providing an electric field generatingapparatus

Aspect 146. The method of aspect 129, wherein providing the body forcegenerating apparatus comprises providing an gravitational accelerationto the first material

Aspect 147. The method of aspect 129, wherein providing the body forcegenerating apparatus comprises providing an acceleration to the firstmaterial

Aspect 148. The method of aspect 147, wherein providing the body forcegenerating apparatus comprises providing an inertial acceleration to thefirst material

Aspect 149. The method of aspect 147, wherein providing the body forcegenerating apparatus comprises rotating the first material

Aspect 150. The method of aspect 147, wherein providing the body forcegenerating apparatus comprises accelerating the first material in aninertial frame

Aspect 151. The method of aspect 147, wherein providing the body forcegenerating apparatus comprises providing a magnetic field generatingapparatus

Aspect 152. The method of aspect 147, wherein the method furthercomprises including or providing a heat exchanger within or to theelectrical circuit, wherein the heat exchanger is configured to deliverthermal energy to at least a portion of mobile charge carriers withinthe electrical circuit

Aspect 153. The method of aspect 147, wherein the method furthercomprises including or providing an electrical switch within or to theelectrical circuit

Aspect 154. The method of aspect 129, wherein the first material cancomprise a solid, liquid, gas, or plasma

Aspect 155. The method of aspect 130, wherein the second material cancomprise a solid, liquid, gas, or plasma

Unless specified or clear from context, the term “or” is equivalent to“and/or” throughout this paper.

The embodiments and methods described in this paper are only meant toexemplify and illustrate the principles of the invention. This inventioncan be carried out in several different ways and is not limited to theexamples, embodiments, arrangements, configurations, or methods ofoperation described in this paper or depicted in the drawings. This alsoapplies to cases where just one embodiments is described or depicted.Those skilled in the art will be able to devise numerous alternativeexamples, embodiments, arrangements, configurations, or methods ofoperation, that, while not shown or described herein, embody theprinciples of the invention and thus are within its spirit and scope.

What is claimed is:
 1. A method of potential energy modification,comprising: providing a body force on charge carriers on a firstmaterial, the body force configured to induce a region of accumulationof charge within the first material, wherein the first material iselectrically conducting, and wherein the first material comprises afirst point and a second point, and wherein the second point is locatedon a boundary of the region of accumulation of charge, and wherein theregion of accumulation of charge has a non-zero electric fieldmagnitude; providing a second material, wherein the second material iselectrically conducting, and wherein the second material comprises afirst point and a second point; and wherein a steady electrical currentcan be made to flow in a closed circuit, wherein the closed circuit isformed when the second point in the first material is electricallycoupled to the second point in the second material and the first pointin the first material is electrically coupled to the first point in thesecond material, and wherein the steady current exceeds the current dueto a Seebeck or Peltier effect; and wherein a relevant property of thesecond material is different relative to the same property in the firstmaterial.
 2. The method of claim 1, wherein a relevant propertycomprises the nominal number of mobile charge carriers per unit volumein a material.
 3. The method of claim 1, wherein a relevant propertycomprises the nominal electrical conductivity of a material.
 4. Themethod of claim 1, wherein the relevant properties comprise the absolutepermittivity within the material.
 5. The method of claim 1, wherein therelevant properties comprise the number of atoms per unit volume.
 6. Themethod of claim 1, wherein the relevant properties comprise the numberof donor atoms or acceptor atoms in a doped semiconductor per unitvolume.
 7. The method of claim 1, wherein the relevant propertiescomprise the temperature of the material.
 8. The method of claim 1,wherein the relevant properties comprise the average charge carried by amobile charge carrier within the material.
 9. The method of claim 1,wherein relevant properties comprise the average effective mass of amobile charge carrier within a material.
 10. The method of claim 1,further comprising: applying a body force on charge carriers on thesecond material, the body force configured to induce a region ofaccumulation of charge within the second material, and wherein thesecond point in the second material is located on a boundary of theregion of accumulation of charge, and wherein the region of accumulationof charge has a non-zero electric field magnitude.
 11. The method ofclaim 10, wherein relevant properties comprise the electric fieldstrength at a boundary of the region of accumulation of charge within amaterial.
 12. The method of claim 1, wherein applying the body forcecomprises subjecting the material to an electric field, wherein at leasta portion of the body force is electric in nature.
 13. The method ofclaim 1, wherein applying the body force comprises subjecting thematerial to a gravitational field, and wherein at least a portion of thebody force is gravitational in nature.
 14. The method of claim 1,wherein applying the body force comprises subjecting the material to amagnetic field, and wherein at least a portion of the body force ismagnetic in nature.
 15. The method of claim 1, wherein applying the bodyforce comprises subjecting the material to an electromagnetic field, andwherein at least a portion of the body force is electromagnetic innature.
 16. The method of claim 1, wherein applying the body forcecomprises subjecting the material to an acceleration in an inertialframe, and wherein at least a portion of the body force is magnetic innature, wherein at least a portion of the body force is inertial innature.
 17. The method of claim 1, wherein the method compriseselectrically coupling the second point in the first material to thesecond point in the second material and electrically coupling the firstpoint in the first material to the first point in the second material.18. The method of claim 17, wherein the electrically coupling comprisesclosing an electrical switch.
 19. The method of claim 17, wherein theelectrically coupling comprises the transmitting of electromagneticenergy.
 20. The method of claim 17, wherein the electrical couplingcomprises providing an electrical load.
 21. The method of claim 17,wherein the method further comprises converting thermal energy intoelectromagnetic energy.
 22. The method of claim 1, wherein the steadyelectrical current can be made to flow when the closed circuit is inthermal contact with a single thermal reservoir.
 23. The method of claim1, wherein the first material or second material can comprise a solid,liquid, gas, or plasma.
 24. A potential energy modification apparatus,wherein the potential energy modification apparatus comprises: a bodyforce generating apparatus, wherein the body force generating apparatusis configured to apply a body force on charge carriers; a firstmaterial, wherein the body force generating apparatus can be configuredto induce a region of accumulation of charge within the first material,wherein the first material is electrically conducting, and wherein thefirst material comprises a first point and a second point, and whereinthe second point is located on a boundary of the region of accumulationof charge, and wherein the region of accumulation of charge has anon-zero electric field magnitude; and a second material, wherein thesecond material is electrically conducting, and wherein the secondmaterial comprises a first point and a second point; wherein a relevantproperty of the second material is different relative to the sameproperty in the first material, and wherein a steady electrical currentcan be made to flow in a closed circuit, wherein the closed circuit isformed when the second point in the first material is electricallycoupled to the second point in the second material and the first pointin the first material is electrically coupled to the first point in thesecond material, and wherein the steady current exceeds the current dueto a Seebeck or Peltier effect.
 25. The potential energy modificationapparatus of claim 24, wherein the first point in the first material islocated in a neutrally charged region within the first material in anopen circuit scenario.
 26. The potential energy modification apparatusof claim 24, wherein the first point in the first material is located ina charged region within the first material in an open circuit scenario.27. The potential energy modification apparatus of claim 26, wherein thesecond point in the first material is located in a charged region withinthe first material in an open circuit scenario.
 28. The potential energymodification apparatus of claim 27, wherein the average charge of thefirst material at the first point is opposite in sign to the averagecharge of the first material at the second point.
 29. The potentialenergy modification apparatus of claim 27, wherein the average charge ofthe first material at the first point is of the same sign as the averagecharge of the first material at the second point.
 30. A systemcomprising two or more of the potential energy modification apparatusesof claim 25, wherein a first potential energy modification apparatus iselectrically coupled in series with a second potential energymodification apparatus.
 31. The system of claim 30, wherein the two ormore potential energy modification apparatuses are arranged in a planararray.
 32. The system of claim 30, wherein the first point in a secondmaterial of a first potential energy modification apparatus iselectrically coupled to the first point in a first material in a secondpotential energy modification apparatus.
 33. The system of claim 30,wherein the accumulation of net charge in the first material at thesecond point consists at least in part of an accumulation of mobilecharge.
 34. A system comprising two or more of the potential energymodification apparatuses of claim 26, wherein a first potential energymodification apparatus is electrically coupled in series with a secondpotential energy modification apparatus.
 35. The system of claim 34,wherein the two or more potential energy modification apparatuses arearranged in a planar array.
 36. The system of claim 34, wherein thefirst point in a second material of a first potential energymodification apparatus is electrically coupled to the first point in afirst material in a second potential energy modification apparatus. 37.The system of claim 34, wherein the accumulation of net charge in thefirst material at the second point consists at least in part of anaccumulation of mobile charge.
 38. The apparatus of claim 24, wherein asteady voltage difference between the first point in the first materialand the first point in the second material can be measured in an opencircuit scenario, wherein the voltage difference is different to thevoltage difference due to a Peltier or Seebeck effect, and wherein theopen circuit scenario comprises an electrical coupling between thesecond point in the first material and the second point in the secondmaterial.
 39. The apparatus of claim 24, wherein the steady electricalcurrent can be made to flow when the apparatus is in thermal contactwith a single thermal reservoir.
 40. The apparatus of claim 38, whereinthe steady voltage difference can be measured when the apparatus is inthermal contact with a single thermal reservoir.
 41. The apparatus ofclaim 24, wherein the first material or second material can comprise asolid, liquid, gas, or plasma.
 42. The apparatus of claim 24, whereinthe apparatus can be configured to convert thermal energy intoelectromagnetic energy.